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Proof step 67 from proof eq-io-truncate (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, boolvar ↔ m2 ≤ n0 ∧ pageno0 ≠ 0 ∧ (m2 / VFS_PAGE_SIZE ∈ content ∨ buf-opt.some?), VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, files[m] = mkfile(m0, md0, m1, content0), buf-opt0 = some(fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n1)), content = content0, dirs0 = dirs1, files0 = files[m, mkfile(n0, md, m1, content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2)], files1 = files[ino, files[ino].content:= (content[pageno1, fill(buf-opt.buf, zero, pageno0, VFS_PAGE_SIZE - pageno0)] upto pageno)], ino = m, new_inode = mkinode(m, md, false, m1, 0, m2), pageno = min(n0, m2), pageno0 = m2 % VFS_PAGE_SIZE, pageno1 = m2 / VFS_PAGE_SIZE, buf-opt.some?, m ∈ files, m2 ≤ n0, m2 % VFS_PAGE_SIZE + n1 ≤ # buf-opt.buf, pageno0 + (VFS_PAGE_SIZE - pageno0) ≤ # buf-opt.buf, VFS_PAGE_SIZE ≥ pageno0, m2 ≤ n0 → pageno0 ≠ 0 → VFS_PAGE_SIZE ≠ 0 ⊦ ⟨afs_inode_sync#(new_inode.size:= n0; dirs1, files1); inode := (m ∈ dirs1 ⊃ mkinode(m, dirs1[m].meta, true, dirs1[m].nlink, dirs1[m].nsubdirs, dirs1[m].size) ;mkinode(m, files1[m].meta, false, files1[m].nlink, 0, files1[m].size) ); err := ESUCCESS; asynced := ?⟩ ( some(fill(buf-opt.buf, zero, pageno0, VFS_PAGE_SIZE - pageno0)) = buf-opt0 ∧ inode = (m ∈ dirs0 ⊃ mkinode(m, dirs0[m].meta, true, dirs0[m].nlink, dirs0[m].nsubdirs, dirs0[m].size) ;mkinode(m, files0[m].meta, false, files0[m].nlink, 0, files0[m].size) ) ∧ boolvar ∧ err = ESUCCESS ∧ dirs1 = dirs0 ∧ files1 = files0), m2 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 68:
# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, files[m] = mkfile(m0, md0, m1, content0), dirs0 = dirs1, files1 = files[m, mkfile(m0, md0, m1, content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE)] upto m2)], m2 % VFS_PAGE_SIZE ≠ 0, buf-opt.some?, m ∈ files, m2 ≤ n0 ⊦ ⟨afs_inode_sync#(mkinode(m, md, false, m1, 0, n0); dirs1, files1); inode := (m ∈ dirs1 ⊃ mkinode(m, dirs1[m].meta, true, dirs1[m].nlink, dirs1[m].nsubdirs, dirs1[m].size) ;mkinode(m, files1[m].meta, false, files1[m].nlink, 0, files1[m].size) ); err := ESUCCESS; asynced := ?⟩ ( fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE) = fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n1) ∧ inode = (m ∈ dirs0 ⊃ mkinode(m, dirs0[m].meta, true, dirs0[m].nlink, dirs0[m].nsubdirs, dirs0[m].size);mkinode(m, md, false, m1, 0, n0)) ∧ err = ESUCCESS ∧ dirs1 = dirs0 ∧ files1 = files[m, mkfile(n0, md, m1, content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2)])

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m; (s)% ⊦ m ≤ n → (n ≤ m ↔ m = n); (s)%⊦ mkfile(m, md, m0, content).content:= content0 = mkfile(m, md, m0, content0); (s)% ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ some(buf) = some(buf0) ↔ buf = buf0; (s)%⊦ mkinode(m, md, boolvar, m0, m1, m2).size:= m6 = mkinode(m, md, boolvar, m0, m1, m6); (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%n ≤ m ⊦ (m - n) + m0 ≤ n0 ↔ m + m0 ≤ n0 + n; (s)%n ≠ 0 ⊦ m % n ≤ n; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)%min-comm: ⊦ min(n0, n1) = min(n1, n0); from specification min-max% ⊦ n0 ≤ n1 → min(n0, n1) = n0; (s)